Instead of just asking about the gap between two consecutive primes, they asked about the gaps between any number of consecutive primes. In 1977 Maier proved that the results concerning the largest distances between two consecutive primes could be proved for each of the gaps between any number of consecutive primes. According to the American Institute of Mathematics, Goldston and Yildrim would have, in a similar way, proved their result for any number of consecutive small gaps, at the same time as they demolished all previous records for one small gap.